ExternalInterface and FireFox issue

I have placed two SWFs on an HTML page using SWFObject.
I originally tried using LocalConnection to pass vars between the two, but found it to be unreliable. So I now use ExternalInterface, passing vars via some JavaScript in the HTML page.
In IE and Safari under Windows all works well.
However, in FireFox the ExternalInterface only works 50% of the time.
On first load of the page it will work. Press F5 to refresh and it fails. Refresh again and it will work.
Admittedly, I dont expect users to refresh the page in this manner. But does anyone have an idea what is happening?